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A154747
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Decimal expansion of sqrt{sqrt{2} - 1}, the radius vector of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
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5
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6, 4, 3, 5, 9, 4, 2, 5, 2, 9, 0, 5, 5, 8, 2, 6, 2, 4, 7, 3, 5, 4, 4, 3, 4, 3, 7, 4, 1, 8, 2, 0, 9, 8, 0, 8, 9, 2, 4, 2, 0, 2, 7, 4, 2, 4, 4, 4, 0, 0, 7, 6, 5, 1, 1, 5, 6, 1, 5, 2, 0, 0, 9, 3, 5, 2, 0, 7, 4, 8, 5, 0, 3, 2, 1, 8, 3, 6, 5, 1, 9, 5, 4, 5, 1, 3, 4, 2, 4, 6, 5, 9, 5
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5
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EXAMPLE
| sqrt{sqrt{2} - 1} = 0.643594252905582624735443437418..., a root of r^4 + 2 r^2 - 1 = 0.
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MATHEMATICA
| nmax = 1000; First[ RealDigits[ Sqrt[Sqrt[2] - 1], 10, nmax] ]
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CROSSREFS
| Cf. A154739 for the abscissa and A154743 for the ordinate.
Cf. A154748, A154749 and A154750 for the continued fraction and the numerators and denominators of the convergents.
Cf. A085565 for 1.311028777, the first-quadrant arc length of the unit lemniscate.
Sequence in context: A118227 A199429 A200104 * A079624 A035335 A011097
Adjacent sequences: A154744 A154745 A154746 * A154748 A154749 A154750
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KEYWORD
| nonn,cons,easy
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AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Jan 14, 2009
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EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 05 2009
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